Guess why books for children use short sentences.
Because they are geared toward people who are still learning the requisite
language skills.
Guess why most programming introductions start with printing Hello, world.
Because they are geared toward people who are still learning the requisite
programming skills. And Mathematical introductions don't begin with
integrals and derivatives either, but that misses the point as entirely
as your two examples.
One of the tasks of a programmer is to manage complexity. The size of a
routine is a trait that is causally unrelated to complexity except in
trivial cases. It is true that relatively shorter routines are often a
by-product of good complexity management, but not by virtue of shortness
itself. The aim should never be about making something smaller, it should
be about making it simpler (and simpler for a routine can be with respect
to several variables, both locally and globally).
$simpler != $shorter;
In fact, as some studies have shown, simpler (in terms of errors, changes
required, and even comprehensibility) is not even correlated with smaller
size (within upper bounds ranging from 100 to 500 line routines).
And with that in mind, I'll paraphrase Einstein:
routines should be made
as simple as possible, but no simpler!. People who equate smaller with
simpler often overshoot the target.
I do not know of any study. I don't care much about studies either, since few are done using the right context and variables.
Well, the head-in-the-sand tactic is a common defense of personal opinion.